and whose face and degeneracy maps are defined by the usual formulas (see (i)–(iii) on page 71 of [1]}).
Note that the family of maps given in degree \(n\)  by \(\sigma _n\colon M_n\rightarrow P_n\) 
defined by \(\sigma _n(m) = (m,1)\)  is a pseudo-cross section. Every PCTP in \(s{K}/B\)  is given by a twisting function in this way.
